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m_a_m_a [10]
2 years ago
14

The number of stamps that kaye and alberto had were in the ratio 5 : 3, respectively. after kaye gave alberto 10 of her stamps,

the ratio of the number kaye had to the number alberto had was 7 : 5. as a result of this gift, kaye had how many more stamps than alberto?
Mathematics
1 answer:
Gala2k [10]2 years ago
4 0
K:A
5:3 (before)
15:9

since the total number of stamps didn't change, the total ratio should be the same.

7:5(after)
14:10

so this means 1 unit is 10stamps.

14-10=4
4 X 10= 40

Kaye have 40 more stamps than Alberto.
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Solve<br> x2 - 8x + 14 = 2x - 7
BabaBlast [244]

Answer:

x=7, x=3

Step-by-step explanation:

             x^{2} -8x+14=2x-7

x^{2} -8x-2x+14+7=0

            x^{2} -10x+21=0

\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}

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positive

x=\frac{-\left(-10\right)+\sqrt{\left(-10\right)^2-4\cdot \:1\cdot \:21}}{2\cdot \:1}

x=7

negative

x=\frac{-\left(-10\right)-\sqrt{\left(-10\right)^2-4\cdot \:1\cdot \:21}}{2\cdot \:1}

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3 years ago
Select all the correct answers. If the measure of angle 0 is 5(pi)/4, which statements are true?
elixir [45]

Finding the equivalent angle of \theta, the correct statements are given as follows:

  • The Measure of the reference angle is 45.
  • \cos{\theta} = \frac{\sqrt{2}{2}}.
  • \tan{\theta} = 1
  • \sin{\theta} = \frac{\sqrt{2}{2}}.

<h3>What are equivalent angles?</h3>

Each angle on the second, third and fourth quadrants will have an equivalent on the first quadrant.

In this problem, the given angle is as follows:

\theta = \frac{5\pi}{4}

It is on the third quadrant, as it is between pi and 1.5 pi, hence the equivalent on the first quadrant, also known as the reference angle, is given by:

\frac{5\pi}{4} - \pi = \frac{5\pi}{4} - \frac{4\pi}{4} = \frac{\pi}{4}

The angle of 45º has equal sine and cosine, and tangent of 1, hence the correct statements are:

  • The Measure of the reference angle is 45.
  • \cos{\theta} = \frac{\sqrt{2}{2}}.
  • \tan{\theta} = 1
  • \sin{\theta} = \frac{\sqrt{2}{2}}.

More can be learned about equivalent angles at brainly.com/question/24787111

#SPJ1

8 0
1 year ago
What is the density of the oak board, it's 5.5 inches wide, 1.5 inches thick , 3 feet long and weighs 8.05 lbs? Please show work
laiz [17]

Answer:

37 - 56 lb / ft3

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Step-by-step explanation:

The density or hardness of wood varies by species, and the value is necessary to approximate the weight of lumber by volume. In this table, the density of different species of wood is expressed as weight in pounds per cubic foot and kilograms per cubic meter. The density will vary based on the moisture content of the wood.

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Cidnee is weighing combinations of geometric solids. She found that 4 cylinders and 5 prisms weigh 32 ounces and that 1 cylinder
vitfil [10]

Answer:

The weights of each cylinder and prism are 3 and 4 ounces, respectively.

Step-by-step explanation:

Let be x and y the masses of a cylinder and a prism, measured in ounces, respectively. After a careful reading of the statement we get the following linear equations by interpretation:

i) <em>She found that 4 cylinders and 5 prisms weigh 32 ounces:</em>

4\cdot x +5\cdot y = 32\,oz (Eq. 1)

ii) <em>And that 1 cylinder and 8 prisms weigh 35 ounces:</em>

x + 8\cdot y = 35\,oz (Eq. 2)

Now we solve the system of linear equations algebraically:

From (Eq. 2):

x = 35 - 8\cdot y

(Eq. 2) is (Eq. 1):

4\cdot (35-8\cdot y) + 5\cdot y = 32

140-32\cdot y +5\cdot y = 32

32\cdot y - 5\cdot y = 140-32

27\cdot y = 108

y = 4\,oz

From (Eq. 2):

x = 35 - 8\cdot (4)

x = 35 - 32

x = 3\,oz

The weights of each cylinder and prism are 3 and 4 ounces, respectively.

4 0
2 years ago
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